Module 5 Summary

In lawn bowling, one team or one player competes against another. Like lawn bowling, many games are competitive. The objective of such games is often for one player or team to achieve a certain objective before the opponent achieves the same objective.

 

There are often steps required to achieve the objectives in a game. In this module you learned to describe the steps needed to solve equations. When solving equations you often have to navigate through several steps in order to find the unknown variable, or the “hidden object.”

 

You investigated the following questions:

• How are rational expressions an extension of rational numbers?
• How can rational expressions be used to model situations related to competition and cooperative games?

The following table summarizes the topics you learned in this module.

 

Lesson 1	Rational expressions can be simplified by dividing the numerator and denominator by a common factor.   Non-permissible values need to be accounted for with rational expressions.
Lesson 2	Rational expressions can be multiplied or divided in a similar manner to rational numbers. When dividing rational expressions, care must be taken to make sure you don’t divide by 0.
Lesson 3	Rational expressions can be added or subtracted in a similar manner to rational numbers. For both operations, a common denominator must be used.
Lesson 4	Rational equations can be solved using processes you learned in previous courses. A good start is to rearrange the equation so it doesn’t have any denominators.
Lesson 5	Some problems can be modeled using rational equations. Often these involve rates and proportions.

 

In this module you investigated rational equations and their applications. You learned that rational expressions must not have denominators equal to 0. As a result, you must identify non-permissible values of the variable when simplifying rational expressions and solving rational equations.

 

The first step in solving rational equations may be to rearrange the equation so it is written without any fractions. Once this is done, the resulting equation will be linear or quadratic. You can then use an appropriate strategy to solve this equivalent equation.

 

This module has addressed the theme of competitive and cooperative games. You learned how to model given scenarios with rational expressions and equations. You discovered how to use rational equations to solve problems related to court dimensions, motion problems, cooperative work situations, and proportions. In the Module 5 Project you reviewed the concepts learned in this module by creating a dice game.